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All sourcesNASA NTRSDOE OSTI
NASA NTRS1999

Determination of Nonlinear Stiffness Coefficients for Finite Element Models with Application to the Random Vibration Problem

In this paper, a method for obtaining nonlinear stiffness coefficients in modal coordinates for geometrically nonlinear finite-element models is developed. The method requires application of a finite-element program with a geometrically non- linear static capability. The MSC/NASTRAN code is employed for this purpose. The equations of motion of a MDOF system are formulated in modal coordinates. A set of linear eigenvectors is used to approximate the solution of the nonlinear problem. The random vibration problem of the MDOF nonlinear system is then considered. The solutions obtained by application of two different versions of a stochastic linearization technique are compared with linear and exact (analytical) solutions in terms of root-mean-square (RMS) displacements and strains for a beam structure.

Muravyov, Alexander A.↗
NASA NTRS1983

Rapid rotation and stellar activity in the triple system HD 165590

X-ray and ultraviolet observations of the spectroscopic and visual binary HD 165590 are presented. Results show that the spectroscopic binary component has a period of 0.88 day and a near-solar spectral type. A substantial soft X-ray flux for HD 165590 is also found with an X-ray luminosity of 10 to the 30.6th ergs/sec for the system. No obvious periodicities of less than 0.5 days are detected in the X-ray data, although stochastic variability is present. Observations of the transition region emission lines using the International Ultraviolet Explorer satellites are shown to be consistent with the X-ray data and reveal an approximately 50% variability on the time scale of days. It is concluded that comparisons of the results for HD 165590 with X-ray observations of other late F and G stars demonstrate that rotation-activity scaling relations are useful as gross predictors of X-ray emission.

Stern, R. A.↗
NASA NTRS1982

On the contribution of a stochastic background of gravitational radiation to the timing noise of pulsars

The influence of a stochastic and isotropic background of gravitational radiation on timing measurements of pulsars is investigated, and it is shown that pulsar timing noise may be used to establish a significant upper limit of about 10 to the -10th on the total energy density of very long-wavelength stochastic gravitational waves. This places restriction on the strength of very long wavelength gravitational waves in the Friedmann model, and such a background is expected to have no significant effect on the approximately 3 K electromagnetic background radiation or on the dynamics of a cluster of galaxies.

Mashhoon, B.↗
NASA NTRS1991

Simulation of the Kolmogorov inertial subrange using an improved subgrid model

A subgrid model is developed and applied to a large-eddy simulation of the Kolmogorov inertial subrange. The subgrid model is based directly on a model of the Navier-Stokes equation. The improved subgrid model contains two terms: an eddy viscosity and a stochastic force. Use of the subgrid model in a forced large-eddy simulation results in an energy spectrum that exhibits a clear k exp -5/3 power-law subrange with an approximate value K(o) = 2.1 of the Kolmogorov constant.

Chasnov, Jeffrey R.↗
NASA NTRS2019

Electron Scattering by Low-frequency Whistler Waves at Earth’s Bow Shock

Electrons are accelerated to nonthermal energies at shocks in space and astrophysical environments. While shock drift acceleration (SDA) has been considered a key process of electron acceleration at Earth’s bow shock, it has also been recognized that SDA needs to be combined with an additional stochastic process to explain the observed power-law energy spectra. Here, we show mildly energetic (∼0.5 keV) electrons are locally scattered (and accelerated while being confined) by magnetosonic-whistler waves within the shock transition layer, especially when the shock angle is large (θ(sub Bn) approximately equal or greater than 70°). When measured by the Magnetospheric Multiscale mission at a high cadence, ∼0.5 keV electron flux increased exponentially in the shock transition layer. However, the flux profile was not entirely smooth and the fluctuation showed temporal/spectral association with large-amplitude (δB/B ~ 0.3), low-frequency (approximately equal or less than 0.1 Ω(sub ce) where Ω(sub ce) is the cyclotron frequency), obliquely propagating (θ(sub kB) ~ 30°–60°, where θ(sub kB) is the angle between the wave vector and background magnetic field) whistler waves, indicating that the particles were interacting with the waves. Particle simulations demonstrate that, although linear cyclotron resonances with ∼0.5 keV electrons are unlikely due to the obliquity and low frequencies of the waves, the electrons are still scattered beyond 90° pitch angle by (1) resonant mirroring (transit-time damping), (2) non-resonant mirroring, and (3) subharmonic cyclotron resonances. Such coupled nonlinear scattering processes are likely to provide the stochasticity needed to explain the power-law formation.

Oka, M.↗
NASA NTRS2003

Stochastic Mixing Model with Power Law Decay of Variance

Here we present a simple stochastic mixing model based on the law of large numbers (LLN). The reason why the LLN is involved in our formulation of the mixing problem is that the random conserved scalar c = c(t,x(t)) appears to behave as a sample mean. It converges to the mean value mu, while the variance sigma(sup 2)(sub c) (t) decays approximately as t(exp -1). Since the variance of the scalar decays faster than a sample mean (typically is greater than unity), we will introduce some non-linear modifications into the corresponding pdf-equation. The main idea is to develop a robust model which is independent from restrictive assumptions about the shape of the pdf. The remainder of this paper is organized as follows. In Section 2 we derive the integral equation from a stochastic difference equation describing the evolution of the pdf of a passive scalar in time. The stochastic difference equation introduces an exchange rate gamma(sub n) which we model in a first step as a deterministic function. In a second step, we generalize gamma(sub n) as a stochastic variable taking fluctuations in the inhomogeneous environment into account. In Section 3 we solve the non-linear integral equation numerically and analyze the influence of the different parameters on the decay rate. The paper finishes with a conclusion.

Fedotov, S.↗
NASA NTRS1991

Compensator design for stability enhancement with collocated controllers

A continuum model rather than a finite element model is used. The optimal compensator design is formulated as a stochastic regulator problem and is shown to be solvable by the general infinite-dimensional theory developed by the author despite the lack of exponential stabilizability. Infinite-dimensional steady-state Riccati equations characterizing the feedback control gain and the Kalman filter gain operators can be solved explicitly. The associated performance indexes including the mean-square control-effort are calculated in closed form. As a first approximation, the compensator transfer function can be realized as a bank of bandpass filters in parallel centered at the undamped mode frequencies. Numerical calculations for the gain and bandwidths for a typical configuration are presented. The performance of the compensator is evaluated when in fact in the true model there is no actuator noise. The theoretical problem involved is to show that the infinite-dimensional stochastic process is asymptotically stationary. It is possible to calculate the steady-state covariance in closed form and thereby calculate performance indexes of interest explicitly, facilitating the choice of optimal design parameters.

Balakrishnan, A. V.↗
NASA NTRS2008

Light Echos in Kerr Geometry: A Source of High Frequency QPOs from Random X-ray Bursts

We propose that high frequency quasi-periodic oscillations (HFQPOs) can be produced from randomly-formed X-ray bursts (flashes) by plasma interior to the ergosphere of a rapidly-rotating black hole. We show by direct computation of their orbits that the photons comprising the observed X-ray light curves, if due to a multitude of such flashes, are affected significantly by the black hole's dragging of inertial frames; the photons of each such burst arrive to an observer at infinity in multiple (double or triple), distinct 'bunches' separated by a roughly constant time lag of t/M approximately equal to 14, regardless of the bursts' azimuthal position. We argue that every other such 'bunch' represents photons that follow trajectories with an additional orbit around the black hole at the photon circular orbit radius (a photon 'echo'). The presence of this constant lag in the response function of the system leads to a QPO feature in its power density spectra, even though the corresponding light curve consists of a totally stochastic signal. This effect is by and large due to the black hole spin and is shown to gradually diminish as the spin parameter a decreases or the radial position of the burst moves outside the static limit surface (ergosphere). Our calculations indicate that for a black hole with Kerr parameter of a/M=0.99 and mass of M=10*Msun the QPO is expected at a frequency of approximately 1.3-1.4 kHz. We discuss the plausibility and observational implications of our model/results as well as its limitations.

Fukumura, K.↗
NASA NTRS1974

Estimation for bilinear stochastic systems

Three techniques for the solution of bilinear estimation problems are presented. First, finite dimensional optimal nonlinear estimators are presented for certain bilinear systems evolving on solvable and nilpotent lie groups. Then the use of harmonic analysis for estimation problems evolving on spheres and other compact manifolds is investigated. Finally, an approximate estimation technique utilizing cumulants is discussed.

Willsky, A. S.↗
NASA NTRS2018

A Summary of Results from Two Full-Scale Fokker F28 Fuselage Section Drop Tests

During 2017, two vertical drop tests were conducted on two partial sections removed from a Fokker F28 MK4000 aircraft as a part of a joint NASA / Federal Aviation Administration (FAA) effort to investigate the crashworthiness characteristics of Transport Category Aircraft, as defined by 14 Code of Federal Regulations, Part 25. The first test was a pure vertical drop test of a relatively uniform forward section, which included an underfloor area for luggage. The second test was a canted drop test onto a sloped surface of a portion of the fuselage representing the wingbox stiffened structure. In both tests, accelerometers were installed on the floor, seat track, luggage, and overhead bin to measure responses in the two airframe sections. In addition, ten Anthropomorphic Test Devices (ATDs, a.k.a. crash test dummies) were included in each test to measure the potential of onboard occupant injury. Self-contained data recorders, logging accelerations and rotational rates, were also used on the seat tracks and lower structure for evaluation as potential crash recording devices in future tests. Finally, the starboard side of each section was painted with a stochastic black and white speckle pattern for use in full field photogrammetric imaging techniques. The results collected show notable differences in the Forward and Wingbox Section responses. The Forward Section floor accelerations showed a relatively uniform response of approximately 7 g throughout the impact event. This section exhibited large amounts of subfloor crushing, floor stiffener failures and seat deformation upon impact. These results are contrasted by the Wingbox Section accelerations, which showed large differences when comparing accelerations recorded from either the rear or the front portion of the section reaching peaks of 39 g in some locations. Additionally, the Wingbox Section test induced a forward motion caused from the rotation at impact. With the exception of the lower cavity, there was minimal deformation in the Wingbox Section, and ATD responses were consistently higher than those for the Forward Section. A complete set of results are presented for the airframe, seat, ATD, overhead bin, and subfloor regions for each section. The ATD results are compared to current injury criteria, and determinations will be made on the likelihood of injury. Additional results for cargo-hold stored luggage are presented in an attempt to provide a component-level characterization for better understanding of under-floor loading. Finally, a discussion of the relevance of the results for a proposed airframe level crashworthiness guideline are presented.

Littell, Justin D.↗
NASA NTRS2014

Simulations of DSB Yields and Radiation-induced Chromosomal Aberrations in Human Cells Based on the Stochastic Track Structure Induced by HZE Particles

The formation of double‐strand breaks (DSBs) and chromosomal aberrations (CAs) is of great importance in radiation research and, specifically, in space applications. We are presenting a new particle track and DNA damage model, in which the particle stochastic track structure is combined with the random walk (RW) structure of chromosomes in a cell nucleus. The motivation for this effort stems from the fact that the model with the RW chromosomes, NASARTI (NASA radiation track image) previously relied on amorphous track structure, while the stochastic track structure model RITRACKS (Relativistic Ion Tracks) was focused on more microscopic targets than the entire genome. We have combined chromosomes simulated by RWs with stochastic track structure, which uses nanoscopic dose calculations performed with the Monte‐Carlo simulation by RITRACKS in a voxelized space. The new simulations produce the number of DSBs as function of dose and particle fluence for high‐energy particles, including iron, carbon and protons, using voxels of 20 nm dimension. The combined model also calculates yields of radiation‐induced CAs and unrejoined chromosome breaks in normal and repair deficient cells. The joined computational model is calibrated using the relative frequencies and distributions of chromosomal aberrations reported in the literature. The model considers fractionated deposition of energy to approximate dose rates of the space flight environment. The joined model also predicts of the yields and sizes of translocations, dicentrics, rings, and more complex‐type aberrations formed in the G0/G1 cell cycle phase during the first cell division after irradiation. We found that the main advantage of the joined model is our ability to simulate small doses: 0.05‐0.5 Gy. At such low doses, the stochastic track structure proved to be indispensable, as the action of individual delta‐rays becomes more important.

Ponomarev, Artem↗
NASA NTRS2014

Simulations of DSB Yields and Radiation-induced Chromosomal Aberrations in Human Cells Based on the Stochastic Track Structure iIduced by HZE Particles

The formation of double‐strand breaks (DSBs) and chromosomal aberrations (CAs) is of great importance in radiation research and, specifically, in space applications. We are presenting a new particle track and DNA damage model, in which the particle stochastic track structure is combined with the random walk (RW) structure of chromosomes in a cell nucleus. The motivation for this effort stems from the fact that the model with the RW chromosomes, NASARTI (NASA radiation track image) previously relied on amorphous track structure, while the stochastic track structure model RITRACKS (Relativistic Ion Tracks) was focused on more microscopic targets than the entire genome. We have combined chromosomes simulated by RWs with stochastic track structure, which uses nanoscopic dose calculations performed with the Monte‐Carlo simulation by RITRACKS in a voxelized space. The new simulations produce the number of DSBs as function of dose and particle fluence for high‐energy particles, including iron, carbon and protons, using voxels of 20 nm dimension. The combined model also calculates yields of radiation‐induced CAs and unrejoined chromosome breaks in normal and repair deficient cells. The joined computational model is calibrated using the relative frequencies and distributions of chromosomal aberrations reported in the literature. The model considers fractionated deposition of energy to approximate dose rates of the space flight environment. The joined model also predicts of the yields and sizes of translocations, dicentrics, rings, and more complex‐type aberrations formed in the G0/G1 cell cycle phase during the first cell division after irradiation. We found that the main advantage of the joined model is our ability to simulate small doses: 0.05‐0.5 Gy. At such low doses, the stochastic track structure proved to be indispensable, as the action of individual delta‐rays becomes more important.

Ponomarev, Artem↗
NASA NTRS1990

Time development of a perturbed-spherical nucleus in a pure supercooled liquid. I - Power-law growth of morphological instabilities. II - Nonlinear development

The linear growth stage of the morphological instabilities developing at the liquid-solid interface during crystal growth from an axisymmetric spherical nucleus is analyzed. The corresponding growth rate parameters are calculated numerically, and it is shown that morphological instabilities for free growth evolve according to a power law in agreement with WKB results and contrary to an exponential law found in a quasi-stationary approximation. The time evolution of an arbitrary perturbed liquid-solid interface from a linear into the nonlinear stage is studied. The initial perturbations include the eigenfunctions for the linear problem, localized perturbations of the grain-boundary type, and a stochastic noise. It is shown that the perturbations grow and spread in a wavelike manner. The formation of a predendritic growth stage is characterized by establishment of constant values of tip radius and velocity.

Pines, V.↗
NASA NTRS1994

Optimal active control for Burgers equations

A method for active fluid flow control based on control theory is discussed. Dynamic programming and fixed point successive approximations are used to accommodate the nonlinear control problem. The long-term goal of this project is to establish an effective method applicable to complex flows such as turbulence and jets. However, in this report, the method is applied to stochastic Burgers equation as an intermediate step towards this goal. Numerical results are compared with those obtained by gradient search methods.

Ikeda, Yutaka↗
NASA NTRS2006

What does reflection from cloud sides tell us about vertical distribution of cloud droplets?

In order to accurately measure the interaction of clouds with aerosols, we have to resolve the vertical distribution of cloud droplet sizes and determine the temperature of glaciation for clean and polluted clouds. Knowledge of the droplet vertical profile is also essential for understanding precipitation. So far, all existing satellites either measure cloud microphysics only at cloud top (e.g., MODIS) or give a vertical profile of precipitation sized droplets (e.g., Cloudsat). What if one measures cloud microphysical properties in the vertical by retrieving them from the solar and infrared radiation reflected or emitted from cloud sides? This was the idea behind CLAIM-3D (A 3D - cloud aerosol interaction mission) recently proposed by NASA GSFC. This presentation will focus on the interpretation of the radiation reflected from cloud sides. In contrast to plane-parallel approximation, a conventional approach to all current operational retrievals, 3D radiative transfer will be used for interpreting the observed reflectances. As a proof of concept, we will show a few examples of radiation reflected from cloud fields generated by a simple stochastic cloud model with prescribed microphysics. Instead of fixed values of the retrieved effective radii, the probability density functions of droplet size distributions will serve as possible retrievals.

Marshak, A.↗
NASA NTRS1986

Heat and mass transfer in flames

Heat- and mass-transfer processes in turbulent diffusion flames are discussed, considering turbulent mixing and the structure of single-phase flames, drop processes in spray flames, and nonluminous and luminous flame radiation. Interactions between turbulence and other phenomena are emphasized, concentrating on past work of the author and his associates. The conserved-scalar formalism, along with the laminar-flamelet approximation, is shown to provide reasonable estimates of the structure of gas flames, with modest levels of empiricism. Extending this approach to spray flames has highlighted the importance of drop/turbulence interactions; e.g., turbulent dispersion of drops, modification of turbulence by drops, etc. Stochastic methods being developed to treat these phenomena are yielding encouraging results.

Faeth, G. M.↗
NASA NTRS1991

Structural factoring approach for analyzing stochastic networks

The problem of finding the distribution of the shortest path length through a stochastic network is investigated. A general algorithm for determining the exact distribution of the shortest path length is developed based on the concept of conditional factoring, in which a directed, stochastic network is decomposed into an equivalent set of smaller, generally less complex subnetworks. Several network constructs are identified and exploited to reduce significantly the computational effort required to solve a network problem relative to complete enumeration. This algorithm can be applied to two important classes of stochastic path problems: determining the critical path distribution for acyclic networks and the exact two-terminal reliability for probabilistic networks. Computational experience with the algorithm was encouraging and allowed the exact solution of networks that have been previously analyzed only by approximation techniques.

Hayhurst, Kelly J.↗
NASA NTRS1991

Probabilistic Structural Analysis Methods (PSAM) for select space propulsion system components

The fourth year of technical developments on the Numerical Evaluation of Stochastic Structures Under Stress (NESSUS) system for Probabilistic Structural Analysis Methods is summarized. The effort focused on the continued expansion of the Probabilistic Finite Element Method (PFEM) code, the implementation of the Probabilistic Boundary Element Method (PBEM), and the implementation of the Probabilistic Approximate Methods (PAppM) code. The principal focus for the PFEM code is the addition of a multilevel structural dynamics capability. The strategy includes probabilistic loads, treatment of material, geometry uncertainty, and full probabilistic variables. Enhancements are included for the Fast Probability Integration (FPI) algorithms and the addition of Monte Carlo simulation as an alternate. Work on the expert system and boundary element developments continues. The enhanced capability in the computer codes is validated by applications to a turbine blade and to an oxidizer duct.

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